I don't mean to invoke any sort of death of the author, the story isn't about anything except what you bring to it kind of vagueness...but part of the genius of Braid is that it's intentionally unclear what the story is about.
The famous quote in the epilogue makes you think of an important historical event, but plausibly that's metaphorical and the game is about something more personal, existential. Maybe the game isn't about anything but making you reflect. Maybe it's an expression of particular events in Blow's life. Maybe all of the above.
There was an interview with Jonathan Blow several years ago in Game Informer, close to when Braid came out. Blow said he'll never explain publicly what the game meant to him so people could have their own explanations not be overshadowed by his authorial intent.
He also said he responded to people who emailed him their interpretation. At the time of the interview only one person correctly guessed Blow's own interpretation.
I can't even imagine what the real answer could be.
I agree, I've played through it twice now and don't think there's anything concrete. Even the "real" ending is just confusing. Still, it's one of the best games I've ever played, for the puzzles alone.
The famous quote in the epilogue makes you think of an important historical event, but plausibly that's metaphorical and the game is about something more personal, existential. Maybe the game isn't about anything but making you reflect. Maybe it's an expression of particular events in Blow's life. Maybe all of the above.